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Solve the following.
Solve: 3tan⁻¹x + cot⁻¹x = π.
Solve: $3\tan^{-1}x + \cot^{-1}x = \pi$.
Answer
Answer
Using $\cot^{-1}x = \frac{\pi}{2} - \tan^{-1}x$:
$3\tan^{-1}x + \frac{\pi}{2} - \tan^{-1}x = \pi$
$2\tan^{-1}x = \frac{\pi}{2}$
$\tan^{-1}x = \frac{\pi}{4}$
Hence $x = 1$.
Final answer: $1$